The 2The 2++ excitation of the Hoyle state in excitation of the Hoyle state in 1212CC

M. ItohCyclotron and Radioisotope Center (CYRIC),

Tohoku University

The 4th GCOE International Symposium on“Weaving Science Web beyond Particle-Matter Hierarchy”,

Tohoku University, Feb. 20th

ContentsContents

● Introduction● Hoyle state and α cluster model● Experimental situations in the world

● Motivation● Experimental setup● Analysis & Result

● Fitting analysis● Multipole decomposition analysis

● Comparison with the result of other experiments● Summary

Hoyle stateHoyle state

The theory of stellar evolution● Triple-α reaction (Bethe,Phys.Rev.55(1939)434)

● Two-step process (E.Salpeter,Astrophys.J. 115(1952)326)

● The third α could be captured through resonance level in12C.(F.Hoyle, Astrophys.J.Suppl. 1(1954)121)

● The 7.65MeV 02

+ state in 12C was found in β-decay of 12BC.W.Cook, W.A. Fowler, C.C. Lauritsen, and T. Lauritsen, Phys.Rev.107(1957)508

3α → 12C + γ

α + α → 8Be (Life time=10-16 sec)8Be + α →12C + γ (non-resonant)

8Be + α → 12C* →12C + γ (resonant)

Hoyle state and α cluster modelHoyle state and α cluster model

●12C, 7.65 MeV 0

2+ = Hoyle state

● Difficult to explain by the shell model● 3α cluster structure (α cluster model)

– Linear chain structure (Morinaga, Phys.Rev.101(1956)254)

– Loosely coupled 3α clusters (gas-like) (3α OCM: Horiuchi,PTP51(1975)1266 )(3αGCM: Uegaki et al,PTP57(1977)1262)(3αRGM: Kamimura,NPA351(1981)456 )

– 3α-clusters condensate in the lowest S-orbit(Tohsaki et al, PRL87(2001)192501)

S-orbit

α cluster

About twice of the 0

1+

The 2The 2++ state around Ex state around Ex～～10MeV in 10MeV in 1212CC

The broad state at Ex=10.3 MeV● Tentatively assigned to be 0+.

● Theoretically,● According to the 3α RGM calculation,

B(E2; 22+→0

2+) = 25 B(E2;2

1+→0

1+)

(Kamimura,NPA351(1981)456)● If the Jπ value of the 10.3 MeV state is 2+,

it should be a member of a rotational band beginning at the Hoyle state.

● One of 3α-clusters enters into the D-orbit in the α condensate model(T.Yamada and P. Schuck, Eur.Phys.J.26(2005)185)

S-orbit

D-orbit

3α7.27

2+?

Result of the β-decay experimentResult of the β-decay experiment

β-decay experiment

Only 0+ and 2+ resonancesThey indicated that the 10 MeV state was not the 2+ state. Ex (2

2+) = 13.9 ± 0.3 MeV,

Γ= 0.7 ±0.3 MeVThe shape of the observed peak at 10 MeV was in good agreement with the R-matrix calculation for the 0+ state H.O.U. Fynbo et al.,

nature433(2005)136

0+

2+

12N(1+) → (12C*) → (8Be(01

+)+α) → 3α

12B(1+) → (12C*) → (8Be(01

+)+α) → 3α

Inelastic α scatteringInelastic α scattering

C.Jaquot et al., Nucl.Phys. A201(1973)247

Left : 12C(α,α')12C*[3α] Eα＝90MeV Emulsion + Dalitz diagram

Center : 12C(α,α') Eα＝240 MeV Texas A&M

(22

+: 11.46 MeV)

Right :12C(α,α') Eα=120MeV KVI (No 2+ state)

(S.Brandenburg, A.Drentje, M.N.Harakeh, and A. van der Wounde,KVI annual report 1985)

Bency John, D.H. Youngblood et al.,PRC68(2003)014305

L=2

L=0

L=0

NACRENACRE

Nuclear Astrophysics Compilation of REaction Rates (C. Angulo et al, Nucl.Phys.A656(1999)3)Widely used when calculating of stellar structure and nucleosynthesis.

http://pntpm.ulb.ac.be/Nacre/nacre.htm

For the triple α reaction, the 9.1 MeV 2+ state in 12Cis included, which is the theoretical prediction in α-cluster model.

(P.Descouvemont and D.Baye, Phys.Rev.C 36(1987)54.)

Motivation

● In inelastic α scattering, angular distributions for the L=0 and L=2 are clearly different around θ ~ 0°.L: Transferred angular momentum

● To identify the Jπ value of the 10 MeV states.

● To give the information of the 2+ state around Ex~10 MeV.

➔ The measurement of 12C(α,α') at extremely forward angles including 0°

DWBA calculation

Experimental setup in RCNPExperimental setup in RCNPFacility:RCNPOsaka University

Reaction:12C(α,α')12C*

Beam:386MeV

Resolution: < 200keV

Angle:0°~10°

Target:12C 3mg/cm2

GRAND RAIDENSPECTROMETER

Energy spectra for Energy spectra for 1212C(α,α')C(α,α')

Fitting analysisFitting analysis

● Energy spectra from 7.4 to12.0 MeV were fitted by several Gaussian functions.

● Angular distributions of the 0

2+, 3

1-, (1-), and

broad bump (03+ + 2

2+?)

were obtained.

Angular distribution of the broad bump around 10 MeV

● The angular distribution was reproduced well with the sum of L=0 and L=2 transitions.

Multipole decomposition analysisMultipole decomposition analysis

● Multipole decomposition analysis (MDA)

● Single-folded optical-potential

● Density-dependent N-α interaction

N-α interaction parametersA. Kolomiets et al., Phys. Rev. C 61, 034312(2000)

Transition densities

● M. Kamimura, Nucl.Phys.A351(1981)456● 0

1+→0

2+ and 0

1+→31

- transition densities obtained by 3α RGM model

● Y. Funaki et al, Eur.Phys.J. A28(2006)259● 0

1+→2

2+ transition density obtained by α condensate model which is

almost same transition density as 3α RGM was used.

Formfactor

01+→0

2+

01+→31

-

01

+→22

+

The results of the MD analysis in The results of the MD analysis in 1212C(α,α')C(α,α')

The results of the MD analysis The results of the MD analysis

03

+ state

Ex = 9.93 ± 0.03 MeV

Γ = 2.71±0.08 MeV

22

+ state

Ex = 9.84 ± 0.06 MeV

Γ = 1.01±0.15 MeV

Result of the Gaussian fit

The result supported to the loosely bound gas-like structure.

● Compare 12C(α,α') datawith the 12C(p,p') spectrum for E

p = 200 MeV

● The 2+ component of the 12C(p,p') data● Ex = 9.6(1) MeV● Γ = 600(100) keV

● The shape of the 2+ peak was a good agreement with the 12C(α,α').

M.Freer et al, Phys.Rev.C 80, 041303(R)(2009)Fig. 4.

Comparison with the Comparison with the 1212C(C(pp,,pp') result') result

Comparison with the 12C(γ,3α) experiment

● M. Gai for the UConn-Yale-Duke-Weizmann-PTB-UCL Collaboration,ActaPhys.Pol.B 42(2011)775

Good agreement with the result of (α,α')

Excitation curve for 12C

The The 44He + He + 88Be reaction rateBe reaction rate

● M.Freer et al, PRC 80, 041303(R)(2009)

SummarySummary

● We have measured inelastic α scattering of 12C at Eα = 386 MeV.

● The angular distributions from θ = 0° to 10 ° around Ex ～ 10　

MeV were continuously obtained.● The angular distribution for the broad bump at Ex ～ 10 MeV was

shown as the sum of the L=0 and L=2 angular distributions.● By the multipole decomposition analysis,

the second 2+ state at Ex = 9.84 ± 0.06 MeV with a width of 1.01 ± 0.15 MeV and the third 0+ state at Ex = 9.93 ± 0.03 MeV with a width of 2.71 ± 0.08 MeV were clearly identified.

● The result is consistent with 12C(p,p') and 12C(γ,3α).

CollaboratorsCollaborators

Kyoto University:H. Sakaguchi, T. Murakami, S. Kishi, Y.Nakatsugawa,

S. Terashima, Y. Yasuda, M. Yosoi, J. Zenihiro, RCNP, Osaka University:M. Fujiwara, N. Hashimoto, K. Kawase, K. Nakanishi,

S. Okumura, Tokyo Industrial Technology: M. Uchida,CNS, Tokyo University: T. Kawabata, Konan University: H. Akimune,University of Notre Dame: U. Garg, B.K. Nayak,

Thank you for your attention